A critique of the term value approach to determining molecular constants from the spectra of diatomic molecules

Two alternative methods for the reduction of observed line positions to spectroscopic constants are compared. In the direct approach, the line positions are fit directly to expressions for the energy level differences in which the upper and lower state molecular constants enter as unknowns. In the traditional term value approach, a two-step procedure is followed where first a set of intermediate unknowns, the upper and lower state term values are calculated from the observed line positions and secondly these term values for each vibrational state, are fit separately to energy expressions in which the molecular constants of that state enter as unknowns. It is shown that there is correlation between the term values of all vibrational states included in the reduction. Thus, the separate fitting of term values to energy level expressions for each vibrational state does not retain this correlation and the molecular constants found in this manner cannot be the minimum-variance, linear, unbiased (MVLU) estimates and the accompanying standard deviations cannot be unbiased estimates. However, if the molecular constants of all the vibrational levels are determined simultaneously from all the term values in a correlated least-squares fit, then the molecular constants will be equal to those determined from the direct approach, i.e., the MVLU set. Furthermore, missing lines and the frequent occurrence of two independent sets of lines within a band both cause the molecular constants obtained from the traditional term value approach to differ even more from the MVLU set. Finally, the limitations of reducing groups of bands simultaneously are discussed. Certain singlet systems are given as examples of the above conclusions.